{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*Initializing next computation from prior result*_\n",
    "\n",
    "This notebook demonstrates using Qiskit Chemistry to plot graphs of the ground state energy of the Hydrogen (H2) molecule over a range of inter-atomic distances using VQE and TwoLocal. It is compared to the same energies as computed by the NumPyMinimumEigensolver and we also compare using the previous computed optimal solution as the starting initial point for the next distance.\n",
    "\n",
    "This notebook has been written to use the PYQUANTE chemistry driver. See the PYQUANTE chemistry driver readme if you need to install the external PyQuante2 library that this driver requires."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing step 20 --- complete\n",
      "Distances:  [0.5   0.525 0.55  0.575 0.6   0.625 0.65  0.675 0.7   0.725 0.75  0.775\n",
      " 0.8   0.825 0.85  0.875 0.9   0.925 0.95  0.975 1.   ]\n",
      "Energies: [[-1.05515973 -1.07591361 -1.09262987 -1.10591801 -1.11628598 -1.12416089\n",
      "  -1.12990476 -1.1338262  -1.13618944 -1.13722136 -1.13711707 -1.13604436\n",
      "  -1.13414766 -1.1315512  -1.12836188 -1.12467175 -1.12056028 -1.11609624\n",
      "  -1.11133943 -1.10634211 -1.10115033]\n",
      " [-1.05515974 -1.07591361 -1.09262987 -1.10591801 -1.11628598 -1.12416089\n",
      "  -1.12990476 -1.1338262  -1.13618944 -1.13722135 -1.13711707 -1.13604436\n",
      "  -1.13414767 -1.1315512  -1.12836188 -1.12467175 -1.12056028 -1.11609624\n",
      "  -1.11133942 -1.10634212 -1.10115033]\n",
      " [-1.05515974 -1.07591361 -1.09262987 -1.10591802 -1.11628599 -1.12416089\n",
      "  -1.12990476 -1.1338262  -1.13618944 -1.13722136 -1.13711707 -1.13604436\n",
      "  -1.13414767 -1.13155121 -1.12836188 -1.12467175 -1.12056028 -1.11609624\n",
      "  -1.11133943 -1.10634212 -1.10115034]]\n",
      "Hartree-Fock energies: [-1.04299622 -1.0630621  -1.0790507  -1.09157046 -1.10112822 -1.10814997\n",
      " -1.11299652 -1.11597525 -1.11734902 -1.11734325 -1.11615145 -1.11393966\n",
      " -1.1108504  -1.10700581 -1.10251056 -1.09745432 -1.09191405 -1.08595588\n",
      " -1.07963694 -1.07300677 -1.06610866]\n",
      "VQE num evaluations: [[366 364 404 408 367 393 395 412 397 350 349 347 365 306 342 408 375 371\n",
      "  358 346 373]\n",
      " [318 442 369 371 350 440 375 351 378 381 347 353 347 366 395 406 352 399\n",
      "  337 478 381]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pylab\n",
    "import copy\n",
    "from qiskit import BasicAer\n",
    "from qiskit.aqua import aqua_globals, QuantumInstance\n",
    "from qiskit.aqua.algorithms import NumPyMinimumEigensolver, VQE\n",
    "from qiskit.aqua.components.optimizers import COBYLA\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "from qiskit.chemistry.drivers import PyQuanteDriver, BasisType\n",
    "from qiskit.chemistry.core import Hamiltonian, QubitMappingType\n",
    "\n",
    "molecule = 'H .0 .0 -{0}; H .0 .0 {0}'\n",
    "algorithms = [{'name': 'VQE'},\n",
    "              {'name': 'VQE'},\n",
    "              {'name': 'NumPyMinimumEigensolver'}]\n",
    "titles= ['VQE Random Seed', 'VQE + Initial Point', 'NumPyMinimumEigensolver']\n",
    "\n",
    "start = 0.5  # Start distance\n",
    "by    = 0.5  # How much to increase distance by\n",
    "steps = 20   # Number of steps to increase by\n",
    "energies = np.empty([len(algorithms), steps+1])\n",
    "hf_energies = np.empty(steps+1)\n",
    "distances = np.empty(steps+1)\n",
    "eval_counts = np.zeros([len(algorithms), steps+1], dtype=np.intp)\n",
    "\n",
    "aqua_globals.random_seed = 50\n",
    "\n",
    "print('Processing step __', end='')\n",
    "for i in range(steps+1):\n",
    "    print('\\b\\b{:2d}'.format(i), end='', flush=True)\n",
    "    d = start + i*by/steps\n",
    "    for j in range(len(algorithms)):\n",
    "        driver = PyQuanteDriver(molecule.format(d/2), basis=BasisType.BSTO3G)\n",
    "        qmolecule = driver.run()\n",
    "        operator =  Hamiltonian(qubit_mapping=QubitMappingType.PARITY, two_qubit_reduction=True)\n",
    "        qubit_op, aux_ops = operator.run(qmolecule)\n",
    "        if algorithms[j]['name'] == 'NumPyMinimumEigensolver':\n",
    "            result = NumPyMinimumEigensolver(qubit_op).run()\n",
    "        else:\n",
    "            optimizer = COBYLA(maxiter=10000)\n",
    "            var_form = TwoLocal(qubit_op.num_qubits, ['ry', 'rz'], 'cz', reps=5, entanglement='linear')\n",
    "            algo = VQE(qubit_op, var_form, optimizer)\n",
    "            result = algo.run(QuantumInstance(BasicAer.get_backend('statevector_simulator'),\n",
    "                                seed_simulator=aqua_globals.random_seed,\n",
    "                                seed_transpiler=aqua_globals.random_seed))\n",
    "            eval_counts[j][i] = result.optimizer_evals\n",
    "            if j == 1:\n",
    "                algorithms[j]['initial_point'] = result.optimal_point.tolist()\n",
    "        \n",
    "        result = operator.process_algorithm_result(result)\n",
    "        energies[j][i] = result.energy\n",
    "        hf_energies[i] = result.hartree_fock_energy\n",
    "\n",
    "    distances[i] = d\n",
    "print(' --- complete')\n",
    "\n",
    "print('Distances: ', distances)\n",
    "print('Energies:', energies)\n",
    "print('Hartree-Fock energies:', hf_energies)\n",
    "print('VQE num evaluations:', eval_counts)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot of ground energies from VQE, whether starting from a random initial point or the optimal solution from the prior point are indistinguisable here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.plot(distances, hf_energies, label='Hartree-Fock')\n",
    "for j in range(len(algorithms)):\n",
    "    pylab.plot(distances, energies[j], label=titles[j])\n",
    "pylab.xlabel('Interatomic distance')\n",
    "pylab.ylabel('Energy')\n",
    "pylab.title('H2 Ground State Energy')\n",
    "pylab.legend(loc='upper right');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(2):\n",
    "    pylab.plot(distances, np.subtract(energies[i], energies[2]), label=titles[i])\n",
    "pylab.plot(distances, np.subtract(hf_energies, energies[2]), label='Hartree-Fock')\n",
    "pylab.xlabel('Interatomic distance')\n",
    "pylab.ylabel('Energy')\n",
    "pylab.title('Energy difference from NumPyMinimumEigensolver')\n",
    "pylab.legend(loc='upper left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets plot the difference of the VQE ground state energies from the NumPyMinimumEigensolver. They are both in the same ballpark and both very small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(algorithms)-1):\n",
    "    pylab.plot(distances, np.subtract(energies[i], energies[2]), label=titles[i])\n",
    "pylab.xlabel('Interatomic distance')\n",
    "pylab.ylabel('Energy')\n",
    "pylab.yscale('log')\n",
    "pylab.title('H2 Ground State Energy')\n",
    "pylab.legend(loc='upper right');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally lets plot the number of evaluations taken at each point. Both start out at the same number since we start them the same. But we can see, as we step along small distances, that the prior solution is a better guess as the starting point for the next step leading to fewer evaluations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(2):\n",
    "    pylab.plot(distances, eval_counts[i], '-o', label=titles[i])\n",
    "pylab.xlabel('Interatomic distance')\n",
    "pylab.ylabel('Evaluations')\n",
    "pylab.title('VQE number of evaluations')\n",
    "pylab.legend(loc='center left');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total evaluations for 'VQE Random Seed' = 7796\n",
      "Total evaluations for 'VQE + Initial Point' = 7936\n",
      "\n",
      "Total evaluations for 'VQE + Initial Point' are 101.80% of 'VQE Random Seed'\n"
     ]
    }
   ],
   "source": [
    "for i in range(2):\n",
    "    print(\"Total evaluations for '{}' = {}\".format(titles[i], np.sum(eval_counts[i])))\n",
    "\n",
    "percent = np.sum(eval_counts[1])*100/np.sum(eval_counts[0])\n",
    "print(\"\\nTotal evaluations for '{}' are {:.2f}% of '{}'\".format(titles[1], percent, titles[0]))"
   ]
  }
 ],
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